M2089897 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	14.2179	68.6567%	500000	15000000	0.1230	5.1502%	14.3409	70.2710%	1.6142%
PrimeNet	2⁵⁸	0.0184	63.7931%	9000	160000	0.0016	2.6753%	0.0200	64.7618%	0.9687%
GPU72	2⁶²	0.2940	66.1290%	9000	140000	0.0015	1.4003%	0.2955	66.6033%	0.4743%
Difference	+5	+13.9239	+2.5277%	+491000	+14860000	+0.1214	+3.7499%	+14.0454	+3.6676%	+3.6676%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.2179

68.6567%

500000

15000000

0.1230

5.1502%

14.3409

70.2710%

1.6142%

PrimeNet

2⁵⁸

0.0184

63.7931%

9000

160000

0.0016

2.6753%

0.0200

64.7618%

0.9687%

GPU72

2⁶²

0.2940

66.1290%

9000

140000

0.0015

1.4003%

0.2955

66.6033%

0.4743%

Difference

+13.9239

+2.5277%

+491000

+14860000

+0.1214

+3.7499%

+14.0454

+3.6676%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2089897	588744883871	12	39.099	140855 5 × 11 × 13 × 197	-	13	197	5.215e-8	2.195e-6	2.522e-6
2089897	13021057280767	14	43.566	3115239 3 × 83 × 12511	2008-09-30	83	12511	7.256e-7	7.247e-5	0.0001
2089897	2940246205210749137	19	61.351	703442850344 2³ × 13 × 193 × 35045977	2016-01-17	193	35045977	0.1789	0.1821	0.3400
2089897	2853179035110519629377	22	71.273	682612357238304 2⁵ × 3 × 7110545387899	2022-01-25	32	7110545387899	417.18	36,934	68,982

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2089897

588744883871

39.099

140855
5 × 11 × 13 × 197

197

5.215e-8

2.195e-6

2.522e-6

2089897

13021057280767

43.566

3115239
3 × 83 × 12511

2008-09-30

12511

7.256e-7

7.247e-5

0.0001

2089897

2940246205210749137

61.351

703442850344
2³ × 13 × 193 × 35045977

2016-01-17

193

35045977

0.1789

0.1821

0.3400

2089897

2853179035110519629377

71.273

682612357238304
2⁵ × 3 × 7110545387899

2022-01-25

7110545387899

417.18

36,934

68,982

exponent	prime factors	composite factor	digits	bits*
2089897	588744883871 13021057280767	7666080856642806456809057	25	82.665
2089897	588744883871 2940246205210749137	1731054910638950935743978469327	31	100.449
2089897	13021057280767 2940246205210749137	38285114257606967823984211948079	32	104.917
2089897	588744883871 2853179035110519629377	1679794559689314710848027825078367	34	110.372
2089897	13021057280767 2853179035110519629377	37151407648457595544612056270292159	35	114.839
2089897	2940246205210749137 2853179035110519629377	8389048830770572115209765475797762597649	40	132.624
2089897	588744883871 13021057280767 2940246205210749137	22540165147582780649892018431909221536533809	44	144.015
2089897	588744883871 13021057280767 2853179035110519629377	21872701181635348281180512068599674537696867489	47	153.938
2089897	588744883871 2940246205210749137 2853179035110519629377	49390095796601688114134042078536988016344878026192 79	52	171.723
2089897	13021057280767 2940246205210749137 2853179035110519629377	10923428535661504650371814428809501059976610624711 6783	54	176.190
2089897	588744883871 13021057280767 2940246205210749137 2853179035110519629377	64311126647012001375482803428610118983373810282220 618035910106993	65	215.288

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-01-17T12:32:58	alpertron	Manual testing	500000	15000000	12		2940246205210749137	19	61.351	0.123	0.275	0.246	5.150%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-01-17T12:32:58

alpertron

Manual testing

500000

15000000

2940246205210749137

61.351

0.123

0.275

0.246

5.150%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-09-30T14:36:00	markr	Manual testing	?	?	13021057280767	43.566	14	1.64932e-7	0.297	3.56886e-7

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-09-30T14:36:00

markr

Manual testing

13021057280767

43.566

1.64932e-7

0.297

3.56886e-7

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.272 GHz-days
Estimated T-Level:	1.300

Digits	B1	Curves	Complete	FacMiss
20	11000	26 / 100	0.260	77.004%
25	50000	26 / 280	0.093	91.117%

New Calculation Method

Total ECM effort:	2.272 GHz-days
Estimated T-Level:	1.300

Digits	B1	Complete	FacMiss
20	11000	0.846	42.903%
25	50000	0.076	92.689%
30	250000	0.005	99.534%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		13	1.106
50000	5000000	2853179035110519629377	6	0.510
50000	6258695		7	0.656

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-05T02:09:48	Oliver Kruse	O2.261	50000	5000000						3	0.255
2019-08-19T19:30:26	Malott	pm12	50000	5000000						3	0.255
2021-09-23T07:51:01	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.595
2022-01-25T09:52:40	MarkS	desktop-i7	50000	5000000	2853179035110519629377	71.273	6	2	7424192921619349	6	0.510
2022-05-15T20:18:09	debrouxl	o9020	50000	6258695						7	0.656

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:33:22

alpertron

Manual testing

588744883871

13021057280767

2940246205210749137

234413471A1150__

2017-10-21T09:23:43

Oliver Kruse

Threadripper

588744883871

13021057280767

2940246205210749137

234413471A1150__

2022-01-28T14:00:01

SRJ2877

LTOS

588744883871

13021057280767

2940246205210749137

2853179035110519629377

17B698205E74C8F9

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront